Paper 2016/462
Fully Homomorphic Encryption with Isotropic Elements
Masahiro Yagisawa
Abstract
In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak point in the enciphering function. In this paper I propose the fully homomorphic encryption scheme with non-zero isotropic octonions. I improve the previous scheme by adopting the non-zero isotropic octonions so that the “m and -m attack” is not useful because in proposed scheme many ciphertexts exist where the plaintext m is not zero and the norm is zero. The improved scheme is based on multivariate algebraic equations with high degree or too many variables while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. The improved scheme is against the Gröbner basis attack.
Note: In previous report 2015/474,2015/733 in Cryptology ePrint Archive, I proposed fully homomorphic encryption which has the weak point in the enciphering function and is not immune from “m and -m attack”. In this report I propose the improved scheme which overcomes the weak point.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Major revision. Masahiro, Y. (2015). Fully Homomorphic Encryption without bootstrapping which was published by LAP LAMBERT Academic Publishing, Saarbrücken/Germany
- Keywords
- fully homomorphic encryptionisotropic octonionmultivariate algebraic equationGröbner basis
- Contact author(s)
- tfkt8398yagi @ hb tp1 jp
- History
- 2016-05-13: received
- Short URL
- https://ia.cr/2016/462
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2016/462,
author = {Masahiro Yagisawa},
title = {Fully Homomorphic Encryption with Isotropic Elements},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/462},
year = {2016},
url = {https://eprint.iacr.org/2016/462}
}
